Contingency Tables

Standards MAFS.9-12.S-ID.2.5 (DOK 2) Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Recognize the differences between joint, marginal, and conditional relative frequencies. Calculate relative frequencies using joint and marginal frequencies. Calculate conditional relative frequencies using joint relative frequencies. Summarize categorical data for two categories in two- way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.

Vocabulary Marginal frequencies: the total frequency for any margin or row. Joint frequencies: the counts in the body of the table

Marginal & Joint Frequencies A two-way table is a powerful tool for examining the relationships between categorical variables. Here are where the joint and marginal frequencies are on the table. Category A Category B Total Category 1 Joint Frequency Marginal Frequency Category 2

Interpreting the table: Sports Video Games Total Male students 7 8 15 Female students 6 2 13 10 23   1. How many total students took the survey? 2. Is this a joint or marginal frequency? 3. How many female students are in the class? 4. How many male students are in the class? 5. Who likes to play sports more than videos, males or females? 6. Are you comparing the joint or marginal frequencies?

Comprehension Check At a high school 23 students are polled to find out who prefers sports to video games. . 7/15 male students prefer sports to video games and 13/23 students prefer sports. Using this data complete the table. What are the marginal frequencies? What are the joint frequencies?

Solution Sports Video games Totals Males 7 8 15 Females 6 2 13 10 23

Now, let’s calculate the relative frequency of this data. Relative frequency is when we compare different classes to the whole; when we want to compare the different classes and the classes to the entire data set. Sports Videos Games Total Male students 7/23 = 30.4% 8/23 = 34.8% 15/23 = 65.2% Female students 6/23 = 26.1% 2/23 = 8.7% 13/23 = 56.5% 10/23 = 43.5% 100%

Creating a two way frequency table 150 Freshman girls and 165 boys were surveyed to choose their favorite subject from the list of Math, English or Science.150 were girls. Of the 115 students that liked math 50 were girls. Of the 130 students that liked science 70 were guys. Complete the table

Now calculate the relative frequency (round to the hundredth when necessary) Create the fraction Make the fraction a decimal ( round to the nearest hundredth when necessary. Make the decimal a percent.

Solution Math English Science Totals Girls 50 50/315 .16 or 16% 40 40/315 .13 or 13% 60 60/315 .19or 19% 150 150/315 .48or 48% Boys 65 65/315 .21 or 21% 30 30/315 .09 or 9% 70 70/315 .22or 22% 165 165/315 .52or 52% 115 115/315 .37 or 37% .22 or 22% 130 130/315 .41or 41% 315 315/315 = 1 or 100%

Relative frequency Analysis The bottom right hand corner is? Data can be displayed in three ways A___________B__________C_________ List the joint relative frequencies ? List the Marginal relative frequencies? How can you tell the difference?

Conditional Relative Frequency Conditional relative frequency has conditions to it. It can tell from the viewpoint of the columns or the rows. So then to calculate we do not use the total as the denominator but the marginal frequency of the row or the column

For example in our chart explain the conditional relative frequencies considering the gender of the students Math English Science Totals Girls 50 50/150 .33 or 33% 40 40/150 .27 or 27% 60 60/150 .40or 40% 150 150/150 or 1 100% Boys 65 65/165 .39 or 39 % 30 30/165 .18 or 18% 70 70/165 .43 or 43% 165 165/165=1 .100% 115 115/315 .37 or 37% 70/315 .22 or 22% 130 130/315 .41 or 41% 315 315/315 = 1

Let’s calculate the conditional relative frequencies considering the favorite subject of the students.

Solution Math English Science Totals Girls 50 50/115 .43 or 43% 40 40/70 .57 or 57% 60 60/130 .46or 46% 150 150/315 .48or 48% Boys 65 65/115 .% 30 30/70 .43 or 43 % 70 70/130 .54or 54% 165 165/315 .52or 52% 115 115/115 = 1 100% 70/70 = 1 130 130/130 =1 315 315/315 = 1

Exit Ticket –Think Pair Share 1 Explain relative frequency. 2. How do marginal relative frequency and joint relative frequency differ? 3 How can conditional frequency be presented? 4.How does a conditional frequency table totals differ from relative frequency totals? Rank yourself on this lesson using these questions? If you ranked lower than a 3 what do you need to do?